Kyungpook Mathematical Journal

  • 제62권2호
  • /
  • Pages.347-361
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  • 2022
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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The Second Reidemeister Moves and Colorings of Virtual Knot Diagrams

  • Jeong, Myeong–Ju (Department of Mathematics, Korea Science Academy) ;
  • Kim, Yunjae (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
  • 투고 : 2020.04.22
  • 심사 : 2022.02.22
  • 발행 : 2022.06.30
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초록

Two virtual knot diagrams are said to be equivalent, if there is a sequence S of Reidemeister moves and virtual moves relating them. The difference of writhes of the two virtual knot diagrams gives a lower bound for the number of the first Reidemeister moves in S. In previous work, we introduced a polynomial qK(t) for a virtual knot diagram K which gave a lower bound for the number of the third Reidemeister moves in the sequence S. In this paper we define a new polynomial from a coloring of a virtual knot diagram. Using this polynomial, we give a lower bound for the number of the second Reidemeister moves in S. The polynomial also suggests the design of the sequence S.

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과제정보

The work was supported by the Ministry of Science, ICT and Future Planning.

참고문헌

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